3-D boundary element–finite element method for velocity–vorticity formulation of the Navier–Stokes equations

Abstract

A numerical method for the solution of the incompressible Navier–Stokes equations was developed using an integral representation of the conservation equations. The velocity–vorticity formulation is employed, where the kinematics is given with the Poisson equation for the velocity vector, while the kinetics is represented with the vorticity transport equation. Based on computational aspects, resulting from CPU time and memory requirements of the boundary domain integral method, a combined approach to the solution of the set of governing equations is proposed. Kinematics is solved using boundary element method (BEM), while kinetics is solved using finite element method (FEM). Lid driven flow in a cubic cavity was considered to show the robustness and versatility of this formulation. Results of Re = 100 , 400 , 1000 show a good agreement with benchmark results.